Question: Factor the following expression: $-5$ $x^2+$ $3$ $x+$ $2$
Explanation: This expression is in the form ${A}x^2 + {B}x + {C}$ . You can factor it by grouping. First, find two values, $a$ and $b$ , so: $ \begin{eqnarray} {ab} &=& {A}{C} \\ {a} + {b} &=& {B} \end{eqnarray} $ In this case: $ \begin{eqnarray} {ab} &=& {(-5)}{(2)} &=& -10 \\ {a} + {b} &=& & & {3} \end{eqnarray} $ In order to find ${a}$ and ${b}$ , list out the factors of $-10$ and add them together. Remember, since $-10$ is negative, one of the factors must be negative. The factors that add up to ${3}$ will be your ${a}$ and ${b}$ When ${a}$ is ${-2}$ and ${b}$ is ${5}$ $ \begin{eqnarray} {ab} &=& ({-2})({5}) &=& -10 \\ {a} + {b} &=& {-2} + {5} &=& 3 \end{eqnarray} $ Next, rewrite the expression as ${A}x^2 + {a}x + {b}x + {C}$ $ {-5}x^2 {-2}x +{5}x +{2} $ Group the terms so that there is a common factor in each group: $ ({-5}x^2 {-2}x) + ({5}x +{2}) $ Factor out the common factors: $ x(-5x - 2) - 1(-5x - 2) $ Notice how $(-5x - 2)$ has become a common factor. Factor this out to find the answer. $(-5x - 2)(x - 1)$